ORDERING TREES BY ALGEBRAIC CONNECTIVITY

Let G be a graph on n vertices. Denote by L(G) the difference between the diagonal matrix of vertex degrees and the adjacency matrix. It is not hard to see that L(G) is positive semidefinite symmetric and that its second smallest eigenvalue, a(G) > 0, if and only if G is connected. This observation led M. Fiedler to call a(G) the algebraic connectivity of G. Given two trees, T1 and T2, the authors explore a graph theoretic interpretation for the difference between a(T1) and a(T2). © 1990 Springer-Verlag.